Saffman-Taylor instability for generalized Newtonian fluids (Article) Publié: Physical Review E: Statistical, Nonlinear, And Soft Matter Physics, vol. 80 p.016308 (2009) PMID 19658807 DOI: 10.1103/PhysRevE.80.016308 WoS: 000268616500052 21 Citations Résumé: We study theoretically the linear Saffman-Taylor instability for non-Newtonian fluids in a Hele-Shaw cell. After introducing the notion of generalized Newtonian fluid we calculate the associated Darcy's law. We derive the relation governing the growth rate of normal modes for a large class of non-Newtonian flows. For shear-thinning fluids at high shear rate our theory provides Darcy's laws free of the nonphysical divergences appearing in the classical approaches. We characterize fluids which develop instabilities faster than Newtonian fluids under the same hydrodynamical conditions. Another primary result that this paper provides is that for some shear-thickening fluids, all normal modes are stable. |